Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods such as compressed sensing. In statistical learning, a class of methods known as structured sparsity regularization seeks to combine both physics-and statisticsbased approaches. Used in bioinformatics to identify genes for the diagnosis of diseases, group lasso is a well-known example. Here in physics, we present group lasso as an efficient method for obtaining robust cluster expansions (CE) of multicomponent systems, a popular computational technique for modeling such systems and studying their thermodynamic properties. Via convex optimization, group lasso selects the most predictive set of atomic clusters as descriptors in accordance with the physical insight that if a cluster is selected, so should its subclusters. These selection rules avoid spuriously large fitting parameters by redistributing them among lower order terms, resulting in more physical, accurate, and robust CEs. We showcase these features of group lasso using the CE of bcc ternary alloy Mo-V-Nb. These results are timely given the growing interests in applying CE to increasingly complex systems, which demand a more reliable machine learning methodology to handle the larger parameter space. arXiv:1910.08086v1 [cond-mat.mtrl-sci]

We investigate the validity of Luttinger's theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger's theorem does not hold in a system of fermions with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. [1,2] showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger's theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and ImG(ω = 0, −∞) = 0. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems. arXiv:1708.08460v4 [cond-mat.str-el]

Recent photoemission spectroscopy measurements [arXiv:1509.01611] on cuprate superconductors have inferred that over a wide range of doping, the imaginary part of the electron self-energy scales as $\Sigma^{\prime\prime}\sim(\omega^2+\pi^2T^2)^a$ with $a=1$ in the overdoped Fermi-liquid state and $a<0.5$ in the optimal to underdoped regime. We show that this non-Fermi-liquid scaling behavior can naturally be explained by the presence of a scale-invariant state of matter known as unparticles. We evaluate analytically the electron self-energy due to interactions with fermionic unparticles. We find that, in agreement with experiments, the imaginary part of the self-energy scales with respect to temperature and energy as $\Sigma^{\prime\prime}\sim T^{2+2\alpha}$ and $\omega^{2+2\alpha}$, where $\alpha$ is the anomalous dimension of the unparticle propagator. In addition, the calculated occupancy and susceptibility of fermionic unparticles, unlike those of normal fermions, have significant spectral weights even at high energies. This unconventional behavior is attributed to the branch cut in the unparticle propagator which broadens the unparticle spectral function over a wide energy range and non-trivially alters the scattering phase space by enhancing (suppressing) the intrinsic susceptibility at low energies for negative (positive) $\alpha$. Our work presents new evidence suggesting that unparticles might be important low-energy degrees of freedom in strongly coupled systems such as the cuprate superconductors.Comment: 10 pages, 7 figure

Expanding the MXene design space from ordered and random double-transition-metal (DTM) MXenes to include high-entropy (HE) MXenes with four or more principal elements enables a powerful approach for enhancing MXene properties. While many DTM MXenes possess unique structures that strongly influence material properties, HE MXenes are largely unknown because they are only recently synthesized. Since certain combinations of transition metals (TMs), e.g., Mo-Ti and Cr-Ti, lead to ordered DTM MXene phases, where Mo/Cr atoms occupy the outer TM layers and Ti atoms occupy the inner layers, it is critical to investigate any possibilities of TM segregation in the atomic layers of HE MXenes. Therefore, we present a high-throughput first-principles study of the atomic configurations of two recently synthesized HE M4C3 MXenes: TiVNbMoC3 and TiVCrMoC3. Combining density functional theory, cluster expansion, and Monte Carlo simulations, we predict a unique preferential occupancy of the TM atoms in the four layers within the single-phase HE MXenes, even at temperatures as high as 2900 K. Across a wide compositional range, the outer (inner) layers are predominantly occupied by two of the four TM elements, with Cr most preferentially occupying the outer layers, followed by Mo, V, Nb, and Ti. The strong compositional dependence of the interlayer segregation highlights the HE MXenes’ tunability. Within each TM layer, the atoms largely form a solid solution, with a tendency for Nb-V separation at lower temperatures. Our results elucidate the chemical order and disorder in HE MXenes, guiding experiments in designing MXenes with enhanced properties within the huge compositional space.